Metabolic function in mammalian tissues is sustained by the delivery of oxygen and nutrients as well as the removal of waste through complex, three-dimensional (3D) networks of hierarchically organized blood vessels. However, fabrication of such 3D vascular networks within soft hydrogels remains one of the greatest challenges in tissue engineering. Sacrificial templates have proven useful for patterning perfusable vascular networks in engineered tissues, but such templates have been constrained in architectural complexity by limitations in the techniques which have been used to fabricate them. We hypothesized that these architectural limitations could be overcome by creating sacrificial vascular templates via selective laser sintering (SLS), an additive manufacturing process which uses a laser to fabricate solid structures from powdered raw materials. We developed an open-source SLS system and demonstrated its capacity to pattern biomimetic scale models of vascular topology. To adapt SLS fabrication for biocompatible and water-soluble materials which could be used sacrificially in the presence of cells, we identified carbohydrate powders formulations which are compatible with SLS and demonstrated laser sintering of carbohydrates into elaborate branched structures, including algorithmically-generated biomimetic branching networks which we term dendritic networks. Laser sintered carbohydrate templates were used to pattern perfusable vascular networks in a range of materials including natural and synthetically-derived biocompatible hydrogels, which can support cells in both the lumenal and parenchymal spaces. We leveraged this methodology to establish a complete pipeline encompassing generative vascular design, additive fabrication, perfusion culture, and volumetric spatial analysis of tissue performance. We identify heterogeneous zones of metabolic activity that emerge in perfused cell-laden hydrogels and we demonstrate that dendritic vascular networks can sustain cell metabolism deep within model tissues greater than 1 cm thick. We also seed endothelial cells, characterize convective transport through dendritic networks, and explore strategies to modulate the dynamics of changing cell densities within perfused gels. Finally, we demonstrate that perfusion culture through dendritic networks can support the survival and function of primary hepatocyte cultures. This approach for rapid design and biofabrication of engineered volumetric tissues offers an experimental strategy for interrogating the relationship between vascular network architecture, metabolite transport, and tissue function.